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n ~ r' n.. _
<br />~' _ r.
<br />- J.1. 1 I ~ r l'-- N~ 1 I'~ L I It It l ^ al . C 11 . tl
<br />, `.y,
<br />' ~ ~ ~ ~~ rr. "' a `_
<br />rti["~ .
<br />a •"c~' t
<br />•..";,• ti
<br />•r'
<br />.. -:-:%-
<br />.,,` ~~
<br />- '~' .
<br />r, < tAx~,
<br />.~ ,~y '~
<br />• I
<br />\i. ~r )
<br />~ [ ~:
<br />i
<br />.+Li 1.+..d:~-.. ~a~ 1'.._, ~` :~.. ;~-~"r.'2~lllt ~'~rrt'J i>!.~LLJ
<br />Fie. ~:__. Photograph of a sliJt in tht eagle} of~the Gros Ventre It icer,
<br />-\'.,o;ning, shooing the mpognphie change after the soil m;ui slippeJ slung a _ •
<br />. - cur~eJ~tailurc surf:ree.
<br />-.:: ,hear for: dF, ii t!ICrtiure nnup.utJ of a term c dl, indentnJent ul
<br />n,vrlal strtii and ;! teen dF, tan d, whi:h is proportion.ll to the nonu:d
<br />..... To sire; lili eal.uLltions, we cumhin: thr part rlF,. tan v with ~[ht
<br />.j .'::t:.ll I„rit :li ihJN'll In FI_L'. ~.~!(/r ), rhl~ tJrie li Jeil~ll:IliJ :li J/~ anJ
<br />1 :.as an ang!eo „it!1 the normal. Tht rtiu!t.lnt of cd! :md r/F ostr the
<br />:^are lallurt surlxe is rcprcitntal by F; and F, rcspecti,el}'.
<br />ThC rC]L'h.r 11I F. Jt the coh CiWO dlilrlbUlCd OIII Wrnll)' alOllg the are ud -
<br />• nnLJ to the unit n,ht,ion tinges the chord, Jist:mx rid, or
<br />"!lis can ht understood fnini the forcei shown in Fig. S 'I(r/). Tht cohevwl
<br />!.m ,rd is the sununation of infinittiinul vectors a~hoie Jirectioni follow
<br />j ..c rc uJ. Thu, their resultant vecwr P, has a nlagniwdt and direction equal
<br />., that of-the chorJ. The line of action of P; must be such that its momrnt
<br />~``.na ans' P,,int (for tunvtniens, point U) ii the saint as [hat of the cghesion
<br />•i,;ributtJ along tht failure surlaee.
<br />The momrnt of the uniformly JistributtJ tohnion along section be of . ,
<br />•~c .Ire is : dl R. Flir the entire length of the arc, it is r•ud R. The moment of
<br />:: resultant F, ii iinlply F,/. Ilcnct, equating the nvo ee have
<br />'- - --, R ty-a.a
<br />
<br />1
<br />-SEl 8.9 ~~SI /1I,N ANA LI'8I5 ,. .~_ _ '• - -_~-I
<br />_ Thus we see that / is larger than R since the arc distance nrl is always lare
<br />- Than the ehoril distance ad. a " ~ _' - ... _
<br />_' ~ The resultant F of F, and F, along arc nrl must pass through poir.:
<br />the intersection of •the vectors F, and IV. Furthermore, as noted in F
<br />8?1(b), dF makes an angle p with the norrnal to t11e failure surface. Thus:tt.
<br />.. resultant F must make an angle approximately equalto pwith the norms;
<br />R'e may takt anothtr approximation and say Fshould be tangent W a tire:'
<br />_ with radius R sin ~ [Fig. S.? I(rr)j. In [Iris way, the directiotl and lint of actic-
<br />-o( the force F.is determined. At (ailure, the three forces Iv, F„ and F ac
<br />in equilibrium, as illustrated by the force polygon in Fig. S.?I(r').
<br />• Failure occurs if we inlacine that the weight II~ is progrssivrly incrt~ia
<br />b}• increasing the density ~ until the equilibrium conditioni ihuwn in FI;
<br />8.?I(c) are fulfillcJ. A more familiar example would be that oC app!}ir--
<br />load at a point, say e, and increasing dlii load until failure oxurs. Since :!.
<br />slip surface is arbitrarily chosen, many slip circles must be trieJ. The rr
<br />e•hic!1 satisfies the failure conditions at the snla!lest ealuc of density is r.
<br />one that will fail fiat. This ii c;llltd the rrirre-ul cirrlr.
<br />Srabilirv number. R'e note that the equilibrium conditions at fz~icr
<br />require that, F, F, and lV'havt the relatiorohip,hown in Fig. S 'I(r). Attu.:.
<br />_: •fict parammttrs arc irrvohed when see consider tht threr torsi F, /', at:,! 1:
<br />_ They arc the shear strength of [he material as reprcstn:e: ~ }ran.! c.::
<br />unit kYl~ht of the Illalel'lal }, aotl IhC dI111tniW ni Jf the ~!JpJ d :111: ;! (F•_
<br />5..?). If four of the five parameters are eiven, the filth one can b: tag. •~!a:c.:
<br />U
<br />r,--__~-
<br />r
<br />r ~ __ __
<br />I
<br />1
<br />I H
<br />r
<br />/
<br />~_ ~+
<br />' rril Pmprrries Gnn wrigM: ~
<br />SlrrnSr h: r - r + s ran a
<br />fib. J.^a. Slope p:vamrteri ine!udcJ in -
<br />' ~ ~ - ~ sea bilit}' number.
<br />Since the tier parameters account for all the physcal proPeniei of a slorr
<br />on a homogeneouf material, their relationship can be ca!eu!ated once at:.
<br />for all. Ta}•lor (1937) publisltcd.tlle results of [Iles[ calculations in the Cyr:;:
<br />of charts. To simplify the pr~`sentation, three of the parantcttrs, r, y, am !r.
<br />arc combined into a new parameter N„ called the srrrhiliq• nunlLer, defined as
<br />r yl/ '
<br />
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